3D Modelling/Projective Geometry

Painting with perspective lines

Perspective Drawing in GeoGebra

Projections of a box on a mirror

Introduction

In this learning module about productive geometry we consider a special application of projections in mathematics, that project a three-dimensional space onto a two dimensional plane. A snapshot with a camera is such a projection, that maps vectors in a three-dimensional space ${ℝ}^3$ onto the image as a two-dimensional space ${ℝ}^2$.

Learning Task

• (Art) Explore, when art discovered a geometrical approach to create paintings that respect construct geometrically the size of objects that appear to smaller on the canvas, if they a far away (see also Perspective Drawing on Mirror).
• (Perspective Drawing) Perform the small course of creating a perspective drawing of a box as a projection of the 3D object on a mirror.
• (Mathematics) Explore the concept of Projective Geometry in general. How does projective geometry generalize the approach of creating a two-dimensional image of objects in the three-dimensional space.

See also

• Perspective Drawing on Mirror
• Projective Geometry